the symmetry of our evidential situation. If our confidence is best modeled by a standard probability function this means that we are to distribute our subjective probability or credence sharply and evenly over possibilities among which our evidence does not discriminate. Once thought to be the central principle of probabilistic reasoning by great..

the symmetry of our evidential situation. If our confidence is best modeled by a standard probability function this means that we are to distribute our subjective probability or credence sharply and evenly over possibilities among which our evidence does not discriminate. Once thought to be the central principle of probabilistic reasoning by great..

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...) independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

Bayesian models typically assume that agents are rational, logically omniscient and opinionated. The last of these has little descriptive or normative appeal, however, and limits our ability to describe how agents make up their minds (as opposed to changing them) or how they can suspend or withdraw their opinions. To address these limitations this paper represents the attitudinal states of non-opinionated agents by sets of (permissible) probability and desirability functions. Several basic ways in which such states of mind can be (...) changed are then characterised and compared with those found in AGM style models of attitude revision. Finally these models are employed to describe how agents make up their mind when deliberating. (shrink)

I will argue for localism about credal assignments: the view that credal assignments are well-defined only relative to suitably constrained sets of possibilities. I will motivate the position by suggesting that it is the best way of addressing a puzzle devised by Roger White.